Artificial materials (metamaterials) with simultaneously negative permeability and permittivity are sometimes called left-handed (LH) materials. LH materials often use arrays of metallic wires and arrays of split-ring resonators or planar transmission lines periodically loaded with series capacitors and shunt inductors. See, e.g., D. R. Smith, W. J. Padilla, D. C. Vier, S. C. Nemat-Nasser, and S. Schultz, “Composite medium with simultaneously negative permeability and permittivity”, Phys. Rev. Lett., Vol. 84, No. 18, pp. 4184–4187, May 2000; G. V. Eleftheriades, A. K. Iyer, and P. C. Kremer, “Planar negative refractive index media using periodically L-C loaded transmission lines,” IEEE Trans. Microwave Theory & Tech., Vol. 50, No. 12, pp. 2702–2712, December 2002; A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens”, Phys. Rev. Lett., Vol. 92, No. 11, p. 117403, 19 Mar. 2004. The unique electrodynamic properties of these materials, first predicted by Veselago in 1968, include the reversal of Snell's law, the Doppler effect, Cherenkov radiation and negative refractive index, making them attractive for new types of radio frequency (rf) and microwave components. V. G. Veselago, “The electrodynamics of substances with simultaneously negative values of ε and μ,” Sov. Phys.-Usp., Vol. 10, No. 4, pp. 509–514, January-February 1968. The most tantalizing is the possibility of realizing “perfect” (diffraction-free) lenses because of their inherent negative index of refraction. R. A. Shelby, D. R. Smith, and S. Schultz, “Experimental verification of a negative index of refraction,” Science, Vol. 292, pp. 77–79, April 2001; A. Grbic and G. V. Eleftheriades, “Overcoming the diffraction limit with a planar left-handed transmission-line lens,” Phys. Rev. Lett., Vol. 92, No. 11, p. 117403, 19 Mar. 2004.
Most studies of LH media are in the linear regime of wave propagation and have already inspired new types of microwave devices, such as LH phase-shifters and LH directional couplers. M. A. Antoniades, G. V. Eleftheriades, “Compact linear lead/lag metamaterial phase shifters for broadband applications”, IEEE Antennas and Wireless Propagation Lett., Vol. 2, pp. 103–106, 2003. C. Caloz, A. Sanada, T. Itoh, “A Novel Composite Right-/Left-Handed Coupled-Line Directional Coupler With arbitrary Coupling Level and Broad Bandwidth,” IEEE Trans. Microwave Theory & Tech., Vol. 52, No. 3, pp. 980–992, March 2004. However, materials that combine nonlinearity with the anomalous dispersion of LH media, can give rise to many new and interesting phenomena and applications. A. A. Zharov, I. V. Shadrivov, Y. S. Kivshar, “Nonlinear properties of left-handed metamaterials,” Phys. Rev. Lett., Vol. 91, No. 3, p. 037401, 18 Jul. 2003. Some nonlinear wave phenomena that occur during propagation along the boundary between right-handed (RH) and LH media, when one or both of them are nonlinear, have been reported in A. M. Belyantsev, A. B. Kozyrev, “RF oscillation generation in coupled transmission lines with anomalous and normal dispersion,” Technical Physics, Vol. 46, No. 7, pp. 864–867, 2001; A. B. Kozyrev, “The structure of a shock electromagnetic wave synchronous with several waves propagating in coupled transmission lines with different types of dispersion,” Technical Physics, Vol. 47, No. 2, pp. 272–274, 2002; A. M. Belyantsev, A. B. Kozyrev, “Reversed Doppler effect under reflection from a shock electromagnetic wave,” Technical Physics, Vol. 47, No. 11, pp. 1477–1480, 2002; I. V. Shadrivov, A. A. Sukhorukov, Y. S. Kivshar, “Nonlinear surface waves in left-handed materials,” Phys. Rev. E, Vol. 69, No. 1, p. 016617, January 2004.